Advanced Mathematical Variants for Estimating Excess Mortality Associated with the COVID-19 and Others Pandemics

The COVID-19 pandemic highlighted the limitations of relying solely on reported COVID-19 deaths to assess its full mortality impact. Excess mortality, defined as the difference between observed all-cause mortality and expected deaths in a counterfactual no-pandemic scenario, provides a more comprehensive and comparable measure across countries. The World Health Organization (WHO) employs generalized additive models (GAMs) with cyclic splines for countries with monthly historical data, log-linear covariate models for data-scarce settings, and clustering-based extrapolation for age-sex patterns. Despite its strengths, this framework exhibits limitations in capturing complex non-linearities, structural changes, mechanistic drivers, and coherent uncertainty propagation across heterogeneous global data. This paper proposes five mathematically advanced variants to enhance excess mortality estimation: (1) structural time series models with Kalman filtering for interpretable decomposition and coherent forecasting; (2) extended SARIMAX models with intervention analysis for handling autocorrelation and abrupt shocks; (3) fully Bayesian hierarchical models with penalized splines and shrinkage priors for principled pooling and full posterior inference; (4) compartmental ordinary differential equation (ODE) models with stability analysis to incorporate transmission-mortality dynamics; and (5) functional principal component analysis (FPCA) combined with functional regression for data-driven, low-dimensional curve representation. Each approach is formally derived, with emphasis on theoretical consistency, uncertainty quantification, and applicability to data-limited settings. We discuss synergies, including multi-model ensembles and hierarchical integration, which could improve global accuracy, robustness, and interpretability. These enhancements offer pathways for evolving WHO methodology, real-time surveillance, and better preparedness for future health crises.